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in this Moon Photography Guide, a F-Number equal to f/11.0 is suggested. In many answers in this forum, similar values are suggested (ranging from f/8.0 to f/11.0). Even if someone suggests f/5.6, it is always much higher than what the DoF formula provides.

Let's do some math. The DoF formula for distant objects is equal to:

enter image description here

It is approximated, but its accuracy is higher as the distance from the subject increases. So, in case of the moon, it should be perfect.

Now,

  • Moon distance from Earth: u = 382500km
  • Required DOF: I'd say the Moon Radius = 1740km
  • Acceptable Circle of Confusion c: I'd say 0.02mm
  • focal length: let's consider 450mm

Hence we need a F-Number N higher than:

N = (450mm ^2) * (1740km) / (2 * (382500km ^2) * 0.02 mm)

This number is several orders of magnitude lower than zero. And it makes sense because of the huge distance between the Moon and the Earth.

So, why not suggesting using the minimum F-Number the lens could provide?

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    \$\begingroup\$ how can a formula with no negatives result in a number lower than zero? \$\endgroup\$
    – ths
    Oct 14, 2022 at 10:40

7 Answers 7

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DoF is a range in front/behind a point of perfect focus. But perfect focus is not achievable/measurable, the best we can get is maximal focus to the resolution limit of the lens or sensor; whichever is lower. So DoF calculations are really already starting with an error/offset. DoF is also extremely biased to the rear of the point of focus at distances ≥ the hyperfocal distance; so a single calculation/radius may not be appropriate.

For something distant like the moon DoF is trivial, as your calculation shows. This is because when an object is distant enough that all light rays entering the lens are parallel the lens will be maximally sharp at any aperture; absent optical aberrations. But (almost?) no lens is optically perfect; even the best lenses need stopped down about one stop to remove optical aberrations generated by the periphery of the objective (greatest bending of light). So even with the best lens the minimum would be about one stop smaller than max. And with many lower quality lenses this number may be f/8-f/11.

For example, this is the Nikkor AF 70-300/4.5-5.6; and you can see that at most focal lengths it is sharpest at f/11 when combined with the sensor resolution (not stated). enter image description here

But also note that sharpness starts to drop off at some smaller aperture due to diffraction (sensor resolution dependent). The choice of "best aperture" is always a tradeoff of fewer optical aberrations against greater diffraction... Or to put it another way; a larger zone of larger details and lower resolution acceptably sharp, VS a smaller zone of smaller details and greater resolution acceptably sharp.

And then there is the question of when are all the light rays entering the lens parallel to the point where aperture is not of consequence? In general that will be the infinity mark (or range) on a lens, and that is typically at around 1000 times the lens' focal length. So focusing anywhere close to the moon would be "at infinity" for any realistic camera lens focal length. But there is a lot of error in attempting to focus at those types of distances.

Notice the distance between 10m - ∞ on this 50mm lens... it is far smaller than the distance between 1.5m - 10m. So even the smallest offset when focusing on the moon could mean many thousands of meters of error. Perhaps even the tolerance of the focus drive mechanism is enough to cause significant error. The appearance of this error is roughly equivalent to optical aberrations of the lens itself (although more uniform); so again, stopping down farther may help to some degree.

enter image description here

Basically, the recommendation to use a smaller aperture is an attempt to correct for the realities vs the theoretical calculations. But the recommendation is also a generality and may not be entirely applicable to your equipment/technique/situation.

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You are over-thinking this problem!

We use depth-of-field math to computer the span of acceptable focus. We agree on an acceptable diameter for the image disks (circles of confusion). Then we compute the distant point and the near point that will be sharply defined. All well and good but---the moon is quite distant. Objects that are positioned more than 3000 times the focal length are at “infinity focus”. Infinity is Latin for as far as the eye can see. Light rays from objects at an infinite distance arrive at the camera as parallel rays. To image, se set the focus distance to the infinity mark (∞). An exception---foreground objects are to be imaged as well as the moon. Given this scenario, we set the focus distance and aperture per the depth of filed math.

In this case, we set the focus at infinity and the aperture at the “sweet spot” of its aperture range. As a rule of thumb, the sweet spot is about two f-stop below the maximum working diameter.

What I am trying to tell you – Set the camera’s focus at infinity and set the aperture at f/8 or f/5.6.

If we use tiny diameter iris settings such as f/16 or f/22, the focus will likely be slightly compromised. This is due to a phenomenon called diffraction. Diffraction will be heightened when we set the iris to a tiny working diameter, tiny apertures degrade because some of the image forming rays from the lens that are cut off by the blades of the iris (aperture) will nevertheless slither around the opening edges an commingle with the mainstream of the image forming rays. This sets up interference that will degrade the image. Thus, we try to avoid the use of super tiny iris settings. Let me add that most time, the degradation is too slight to be distinguished.

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    \$\begingroup\$ Don't set the camera’s focus at infinity, actually focus! The mechanical infinity stop has too much slop. \$\endgroup\$ Oct 15, 2022 at 17:08
  • \$\begingroup\$ @user10216038: You do need to set the cameras focus at infinity, i.e. when parallel rays are in focus. It's almost never the setting indicated by the ∞ symbol, though. Lens makers usually add a small range after ∞, in order to be sure you can still focus far away objects if there's any slop, as you said. \$\endgroup\$ Oct 16, 2022 at 9:05
  • \$\begingroup\$ @EricDuminil You do need to set the cameras focus at infinity, i.e. when parallel rays are in focus. Not true, when focusing on the moon. With long lenses at wide-open aperture, there is a noticeable difference in focusing on the moon vs. focusing on more distant objects like Jupiter, or stars. The difference in focus is very slight, but it is noticeable in the final image. \$\endgroup\$
    – scottbb
    Feb 2, 2023 at 3:33
  • \$\begingroup\$ @scottbb [citation needed]. Feel free to apply the lens formula, and notice that what you claim cannot possibly be the case. JWST has a focal length of 130000mm, and doesn't bother to focus. space.stackexchange.com/a/58766/19229 . Your "noticeable difference", if it exists, cannot be explained by geometry. \$\endgroup\$ Feb 2, 2023 at 4:17
  • \$\begingroup\$ @EricDuminil JWST focuses on deep space objects, which are effectively at infinity relative to near solar system objects. \$\endgroup\$
    – scottbb
    Feb 2, 2023 at 4:37
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Actually, the depth of field isn't the only consideration.

When you are photographing moon, focusing is difficult. Many cameras, especially older, only have contrast detect autofocus which is very slow and cumbersome, when photographing from the screen. The moon is almost always so small that getting viewfinder focus point exactly on the moon is bit difficult. Manual focusing can be done, but then there's always limited accuracy on that, even if you magnify the image on the screen. About the only case where you can say focusing is easy is when you have a recent mirrorless camera with dual pixel autofocus.

So you can almost always say that the focus is slightly off. Just slightly, but still off.

By using a small aperture (large F-number), you allow more focus misalignment before it becomes too much of a problem. Wide open, very slight focus misalignment would create a blurry image. Stopped down, not so much.

Another benefit is that lenses are usually sharper when you stop them down. Sharpness is very important with moon photography, because almost always your lens has so short focal length moon covers only very small area of the whole frame. And even if you have enough focal length, it's usually achieved through teleconverters, which add focal length but don't add lens sharpness. So therefore the teleconverter is magnifying lens imperfections, and you want as little of those imperfections as you can have. Thus, you stop the lens down to get as much sharpness as you can.

The moon is bright. In fact, it's as bright as sunlight because the moon is lit by the sun. Therefore, lack of light isn't a problem. With star photography for example, you want to capture as much light as you can and therefore you use fast lenses.

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    \$\begingroup\$ I sort of agree with this, although in live view you can zoom in to focus (if you have a very steady tripod....). Another question is what is the soft spot for the color aberrations? Shooting the moon is a very good way to test your lens for this... (even if in post-prod you can extract just one of the channels and recolor it....) \$\endgroup\$
    – xenoid
    Oct 12, 2022 at 21:27
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    \$\begingroup\$ "So you can almost always say that the focus is slightly off." Hmmm, no? You could simply focus on a bright star or planet. It's really easy to tell if they're sharp or not, especially with live-view. Once you get critical focus, you can simply move to manual focus mode, and be sure that all your moon pictures will be as sharp as the atmosphere allows. \$\endgroup\$ Oct 13, 2022 at 7:15
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    \$\begingroup\$ @EricDuminil It's actually quite difficult because you make the camera shake while adjusting the focus (unless you have a camera with electric focus). \$\endgroup\$
    – xenoid
    Oct 13, 2022 at 10:52
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    \$\begingroup\$ @xenoid: I'm not sure what to tell you. I've done it many times, and it worked perfectly fine. Camera shake isn't a problem, because a few millimeters most won't change the moon-camera distance. If camera shake is a problem, simply put the camera on a tripod. And the whole process is easier and faster without any autofocus. Live-view + manual focus works fine. \$\endgroup\$ Oct 13, 2022 at 11:47
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    \$\begingroup\$ @EricDuminil I have a reasonably good tripod, but at 560mm on APS-C you have better not touch the camera (I use the remote to take the picture). When you touch the lens for focus you get several pixels of shake amplitude (so until the shake has subsided you can't see the effect of your change), and in the meantime the moon has drifted a bit across the screen (it drifts by its diameter in two minutes....). \$\endgroup\$
    – xenoid
    Oct 13, 2022 at 12:16
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Short answer:

When you are shooting the Moon, you need to set your focus to infinity, so DoF also tend to infinity. This suggestion has nothing to do with the DoF but other properties of an optical system.

Long answer:

What you refer to is known as "Loony-11" technique, which suggests that you stop your aperture down to f/11, then shoot using shutter speed which is inverse of ISO speed, regardless of your focal length. Fir instance, if You select ISO800, your shutter speed should be set to 1/800. You don't want to shoot with low ISO and low shutter speeds to achieve low noise, because the Moon is not standing still, it's moving across the sky at rate close to 15 arcsec per second and with long focal length this movement become soon visible in form of motion blur.

Loony-11 rule is general rule. Every rule has exceptions, but it's what will work for most setups.

Key point here is f/11, because of two reasons:

First reason is imperfections of optical systems. Most lenses are not sharp widely open, some of them will achieve peak sharpness after one or two f stops, after f/8 most of them will be as sharp as they go (rule f eight is your friend), but to be sure, after f/11 almost all lenses are as sharp as they can be.

Second reason is chromatic aberration. You can't focus all three channels using common achromatic lens, but most likely two of them. Stopping down your lens will reduce this effect and avoid blurring your image due to channels which are not in focus, commonly blue channel.

Using such small aperture will introduce some vignetting but it's not important since you are shooting bright object in center of your field of view.

There are better techniques, but they are dependent on properties of the setup you are imaging with, like optical system, sensor size, pixel pitch, focal projection size, projection angle, etc. With Loonly-11 your don't need a degree in optometric studies to produce good image.

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From point of view of DoF you do not need F8 or similar. It is just easy to remember, I use F8, ISO100, 1/100 (similar to Sunny 16 rule). So you can use (for example) F4 and set speed to 1/400.

But there is another point of view. Most (if not all) lens are sharpest somewhere in the middle of aperture range. So setting F8, F9, etc will provide you the sharpest image. Also you will need as much as possible sharpness because the light will be distorted by ~10000 kilometers of air.

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    \$\begingroup\$ 10,000 km of air? Hardly, even when the moon is just above the horizon and the line of sight is almost tangent to the Earth' surface. Half of the atmosphere's density is within 5.5 km of sea level, the next 0.25 is within 10.5 km of sea level. The entire amount of material from the Karman line (100km) to the edge of the exosphere is equal to that contained in only a few inches at sea level. \$\endgroup\$
    – Michael C
    Oct 13, 2022 at 2:47
  • \$\begingroup\$ @MichaelC, I get the number from National Geographic. And even 1 km air can change the light. education.nationalgeographic.org/resource/atmosphere \$\endgroup\$ Oct 13, 2022 at 4:36
  • \$\begingroup\$ Well, it's rather the opposite: if you're going to lose sharpness because of the air, it's pointless to hunt for maximum lens sharpness. \$\endgroup\$
    – Zeus
    Oct 14, 2022 at 0:30
  • \$\begingroup\$ @RomeoNinov Yes, even one km of air can affect the shot to one degree or another, depending on the atmospheric condition. But that doesn't prove anything regarding the claim that one must shoot through 10,000km of air to take a photo of the Moon. \$\endgroup\$
    – Michael C
    Oct 15, 2022 at 23:58
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Quite simply, photographing the moon from earth will never be subject to depth of field issues, at all.

Using your numbers, the required depth of field of the moon is 38,1630 ± 870 km (38,1630 km ± 0.228%). And because the focus distance of 38,000 km is almost 6 orders of magnitude larger than the lens's focal length of 450 mm, the object of interest (i.e., the moon) is effectively a flat plane. There is no way you can detect difference in focus distance from the rim of the moon and the center of the moon (a focus distance difference of 1740 km) with any earth-bound 450 mm lens on a camera system with 0.02 mm circle of confusion.

Additionally, practically speaking, the fastest lens you can use might get to less than f/1. But at ~450 mm, good luck finding a lens faster than f/4.

As other answers mentioned, the reason the moon is recommended to be photographed around f/11 or so is because it's really bright. Because DoF isn't a concern, the camera's aperture is merely an exposure control, in addition to the reality that lenses perform better between f/5.6 – f/11 (depending on the specific lens). It's all about image quality and exposure control.

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Practically speaking the sharpness of moon photos is not limited by depth of field as your calculation shows, but by „seeing“. Seeing is caused by the inherent movement of the earth’s atmosphere, same a the flirring and flickering you experience on a hot summer day over a hot road. It also causes stars to twinkle.

The way to overcome seeing is by Lucky Imaging, taking many short exposures and using only a fraction of them and combining the sharpest areas in that subset by using software (best known are Autostakkert, Registax, and PlanetarSystemStacker).

The aperture you choose for that is the largest you have available for your given focal length, to minimise exposure time. Most telephoto lenses or telescopes are f/5 and up: Given that you need 1500mm for an APSC sensor to have a full frame moon (roughly), a f/3 meant a diameter of 500mm and that is expensive. Typical Schmidt-Cassegrain or Maksutov telescopes for planetary imaging start with 150mm aperture at 1500mm focal length (f/10).

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